SOLUTION: Need help factoring this, not solving. 2a^2-11a+7

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Question 649634: Need help factoring this, not solving.
2a^2-11a+7
Found 2 solutions by solver91311, swincher4391:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


This does not factor over the rationals. If you want to factor over , then the easiest thing to do is to solve using the quadratic formula to get the two real roots and . Then write your two factors and

John

My calculator said it, I believe it, that settles it
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Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
In order to factor this expression, you must use the quadratic formula. From the solution, you can factor this since there are no rational solutions to this equation (if set to 0).
Before we go through this, it's easy to see that if we did have rational solutions, we'd have a (2a?7) and a (a?1) as our factors where ? is either + or -. We can further deduce that both must be - since the middle term is negative.
This means that we have (2a-7)(a-1); however, if we check this, we get 2a^2 -7a -2a +7 = 2a^2 -9a +7
So let's use the quadratic formula: for ax^2+bx+c
a = 2 b = -11 c = 7
%2811+%2B-+sqrt%28121+-56%29%29%2F4+=+%2811%2B-sqrt%2865%29%29%2F4
This means that x-(11+sqrt(65))/4 = 0 and x-(11-sqrt(65))/4 = 0
Multiply both sides by 4 to get
4x+-11+%2B+sqrt%2865%29 = 0 and 4x+-+11+-sqrt%2865%29+=+0
So to factor this we have %281%2F8%29%284a%2Bsqrt%2865%29-+11%29%284a-sqrt%2865%29-11%29 <---answer
FOIL this out to get (1/8)(16a^2 -88a +56) = 2a^2-11a+7. Good.